Postgraduate

Modules

Modules

MAS8384 : Bayesian Methodology

Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

Bayesian inference provides an ideal approach for synthesizing information from different sources in a coherent way. In recent years great advances have been made in the application of Bayesian statistical inference to problems across a wide variety of areas within industry, such as drug development, voice recognition and credit card fraud detection. This has been made possible by the development of computational algorithms which allow posterior distributions to be found in complicated models. This module starts with an introduction to the principles of Bayesian inference before moving on to address the fundamental practical problem of calculating the posterior distribution for complex models. The theory behind some modern Bayesian computational methods, which provide a simulation-based solution, is developed and put into practice using R.

Specifically, the module aims to equip students with the following knowledge and skills:
- To gain an understanding of the principles of the Bayesian approach to inference and experience in the application of Bayes rule to update a prior distribution to a posterior distribution using a likelihood function.
- To gain an understanding of the theory behind some modern Bayesian computational methods for approximating a posterior distribution and practical experience of their application in R to solve a variety of applied problems.

Outline Of Syllabus

- Conjugate Bayesian inference
- Non-conjugate models
- Markov chain Monte Carlo (MCMC): methods such as Gibbs sampling, Metropolis-Hastings sampling, slice sampling; assessment of mixing and convergence
- Posterior summaries
- Applications, such as linear models, generalized linear models, mixture models, hidden Markov models, dynamic linear models, Gaussian process regression
- Computation using R and R packages such as rjags

Teaching Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

Teaching Activities
Category Activity Number Length Student Hours Comment
Structured Guided LearningLecture materials32:307:30Structured non-synchronous practical
Structured Guided LearningLecture materials91:3013:30Non-synchronous online pre-recorded lectures and set reading
Guided Independent StudyAssessment preparation and completion214:0028:00Formative and summative reports
Scheduled Learning And Teaching ActivitiesPractical31:304:30Present in person structured synchronous practical
Guided Independent StudyProject work128:3028:30Main project
Scheduled Learning And Teaching ActivitiesDrop-in/surgery31:304:30Virtual office hour, synchronous on line
Guided Independent StudyIndependent study91:3013:30Lecture follow up/background reading
Total100:00
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Practicals are used both for solution of problems and work requiring extensive computation and to give insight into the ideas/methods studied; they are also used to discuss the course material, identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. The project allows the students to develop their problem solving techniques and practise the methods learnt in the module.

Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

The format of resits will be determined by the Board of Examiners

Other Assessment
Description Semester When Set Percentage Comment
Practical/lab report2M40Individual report
Report2M60Main module project
Zero Weighted Pass/Fail Assessments
Description When Set Comment
Oral PresentationMA 3 min video articulating the main findings of one aspect of the coursework report
Formative Assessments
Description Semester When Set Comment
Practical/lab report2MA compulsory report allowing students to develop problem solving techniques, to practise the methods learnt and to assess progress
Assessment Rationale And Relationship

Written assignments (3 pieces of work of equal weight) followed by a larger piece of project work allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback.

The semi-structured oral examination facilitates a reflective discussion about how individual students have met the learning objectives of the module and how the principles of fundamental statistics are embedded in the functionality of their project work.

Reading Lists

Timetable